Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
Problem 6.65
Textbook Question
Textbook QuestionUse a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = cot⁻¹ (―0.92170128)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as cotangent inverse (cot⁻¹), are used to find the angle whose cotangent is a given number. These functions are essential for solving equations where the angle is unknown. The output of these functions is typically restricted to a specific range to ensure that each input corresponds to one unique output.
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Cotangent Function
The cotangent function is defined as the ratio of the adjacent side to the opposite side in a right triangle, or as the reciprocal of the tangent function. It is important to understand how cotangent behaves, especially in different quadrants, as this affects the values returned by its inverse function. The cotangent function is periodic and has specific asymptotes where it is undefined.
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Radian Mode in Calculators
Calculators can operate in different modes, with radian mode being crucial for trigonometric calculations in higher mathematics. When in radian mode, angles are measured in radians rather than degrees, which is essential for accurately computing values of trigonometric functions and their inverses. Understanding how to switch between modes and the implications of each is vital for correct calculations.
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